Shown below is a configuration of FOUR solid spheres each of radius 40cm that are placed on four corners of a regular tetrahedron with side 120cm. The centres of the spheres coincide with the corners of the tetrahedron. What is the radius (in cm) of the largest sphere that can be accommodated within the tetrahedron?

Shown below is an image of a circle and six equilateral triangles. The circumference of the circle is 18.85 cm. What is the area of ONE equilateral triangle in cm2? Assume √3 = 1.732 and π = 3.14.

A vehicle with a wheel arrangement is shown in Figure (i). This vehicle is travelling along a circular path as shown in Figure (ii). The wheels do not change their orientation while moving along the circular path. Figure (iii) shows the location of the centres of the wheels. The…

If SQ = QR = RS = SP = PQ and PR = 21 units, what is the area of the BLACK portion? (Assume π = 22/7)

A tank with internal dimension 10 cm x 10 cm x 10 cm (length x width x height) is fully filled with spherical marbles, each marble having a diameter of 1 cm. Each layer of marbles should have equal number of marbles. Water is then poured into the tank. What is the volume of water…

The bold lines correspond to four different paths P, Q, R and S. What is the length of the longest path? The length of each side of the square grids is 7 units. Use 22/7 as the value for π.

The image shows the profile of the blade which is designed to turn a wooden block, rotating about the axis PQ. Calculate the volume of the turned wooden block between P and Q. Consider the value of π to be 22/7.

A blue colour liquid is used completely to make a star shaped jelly using the mould shown on the right. What is the value of ‘X’ in cm? Ignore the wall thickness of the mould and consider the value of π to be 22/7.

Shown below are four sides of a rectangular dice. If 3 such dice are thrown together, what is the probability of getting a total sum of 4? Consider the value of the blank side to be zero.